Answer:
The slope of line u is -(4/9)
Explanation:
Perpendicular lines have slopes that are the negative inverse of each other. That is, for example, if line B has a slope of 2, a perpendicular line (line B) would have a slope of -(1/2).
Lets find the equation of the line that goes through points (4,1) and (8,10). We'll look for an equation with the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x = zero).
Slope is the Rise/Run between two points. Line A:
Rise = (10 - 1) = 9 [ y increase by 9 when x goes from 4 to 8].
Run = (8 - 4) = 4 [x increase by 4 between the two points.
Slope (m) = (Rise/Run)
Slope (m) = -(9/4)
The equation takes the form y = (9/4)x + b
b can be calculated by entering a point that is on the line and solving for b:
y = (9/4)x + b
1 = (9/4)(4) + b for (4,1)
1 = 9 + b
b = -8
The full equation is y = (9/4)x - 8)
Line u is perpendicular to this line, so its slope will be the negative inverse of line t, or -(4/9)
See the attached graph.